ON MINIMAL COSET COVERING OF SOLUTIONS OF A BOOLEAN EQUATION - Minasyan, A.V. (Proceedings of the YSU A: Physical and Mathematical Sciences, 2015)
For the equation $x_1x_2… x_n+x_{n+1}x_{n+2}… x_{2n}+x_{2n+1}x_{2n+2}… x_{3n}=1$ over the finite field $F_2$ we estimate the minimal number of systems of linear equations over the same field such that the union of their solutions exactly coincides with the set of solutions of the equation. We prove in this article that the number in the question is not greater than $9n^{\log_{2} 3}+4$.
Keywords: linear algebra, covering with cosets, blocking set